Suspension rheology of adhesive particles at high shear-rates

A scaling relationship is developed for the asymptotic approach of the suspension viscosity of adhesive, rigid, and non-Brownian particles to that of nonadhesive particles in the limit of high shear-rate where the agglomerates are broken down completely. The relationship is fitted to experimental data for spherical particles, irregularly shaped particles, and biconcave, discoid-shaped, hardened red blood cells. The relationship allows us to extract a proxy for the interparticle adhesion force, which, for the case of the blood cells, is in qualitative agreement with alternative force measurements in the literature.

Figure 1

(a) Particle radius distribution measured by laser diffraction for spherical particles and irregularly shaped particles. (b) SEM image of spherical particles. (c) SEM image of irregularly shaped particles.

Figure 2

Photograph of (agglomerates of) spherical silica particles for $\varphi =0.01$ in mineral oil, sheared at $\dot{\gamma }=50 {\mathrm{s}}^{-1}$ (a) and at 500 ${\mathrm{s}}^{-1}$ (b) and of irregularly shaped silica particles for $\varphi =0.01$ in mineral oil, sheared at $\dot{\gamma }=20 {\mathrm{s}}^{-1}$ (c) and at 500 ${\mathrm{s}}^{-1}$ (d).

Figure 3

(a) Relative viscosity, (b) infinite viscosity, (c) virial viscosity, and (d) adhesion proxy $F^{\prime }$ [Eq. (7b) using $\delta =0.5$]. The open symbols are the spherical particles for $\varphi =$ 0.02 ($\circ$), 0.03 ($\square$), 0.04 ($▿$) and the filled symbols are the irregularly shaped particles for $\varphi =$ 0.02 ($•$), 0.03 ($\blacksquare$), 0.05 ($▾$). The error bars in (a) are smaller than the marker sizes. The dashed line in (b) is the Batchelor relation ${\eta }_{r,\infty }=1+2.5\varphi +5.2{\varphi }^2$. The dashed lines in (c) have slopes of $-0.5$ and represent Eq. (4) with $\delta =0.5$. The horizontal dashed lines in (d) indicate Eq. (7b) with $\delta =0.5$.

Figure 4

Adhesion proxy $F^{\prime }$ [Eq. (7b) using $\delta =0.5$] as a function of the shear-rate $\dot{\gamma }$ at different particle volume fractions $\varphi$. Open symbols are 110 nm diameter silica spheres in mineral oil for $\varphi =$ 0.05 ($\circ$), 0.1 ($\square$), and 0.15 ($▿$) [11]. Filled symbols are 21 $\mu \mathrm{m}$ diameter silica spheres in mineral oil for $\varphi =$ 0.15 ($•$), 0.2 ($\blacksquare$), 0.25 ($▾$), and 0.30 ($▸$) [11].

Figure 5

Adhesion proxy $F^{\prime }$ [Eq. (7b)] using $\delta =0.55$ for RBC 75 (open symbols) and $\delta =0.6$ for RBC 150 (filled symbols) as a function of the shear-rate $\dot{\gamma }$ for different RBC volume fractions $\varphi =$ 0.13 ($\circ$ and $•$) and 0.21 ($\square$ and $\blacksquare$) [6].